While the world was holding its breath for the birth of the royal baby earlier this week, some businesses were counting on Prince William and wife Kate Middleton's bundle of joy to bring them bundles of cash.

From royal onesies to commemorative plates, an astonishing assortment of royal baby-themed merchandise appeared in the weeks before Prince George's arrival on Monday. Upscale London department store Harrod's has already sold out of its royal baby-themed decorative plate and mug. Meanwhile, enterprising individuals such as artist Lydia Leith have also joined the baby craze, selling royal baby sick bags.

Analysts say the sale of such merchandise, along with increased tourism and other economic activity, will provide an estimated $400-million boost to the British economy.

But we may soon be approaching "peak baby." News events like this one often generate short-lived demand among consumers. So how can business owners benefit from the bubble and not get hurt when it pops? The simple answer: by planning their inventory carefully and using estimates based on past events.

But planning for a one-off event like the birth of a royal heir is hardly simple. "Each one of these events is unique, so it's hard to anticipate how much you'll be able to sell," says David Reibstein, a professor of marketing at the Wharton School of the University of Pennsylvania and the co-founder of BizRate.com.

Annual sporting events such as the Super Bowl also generate tremendous amounts of tie-in merchandise, for which the demand is easier to predict, he says. This is because the event happens regularly, allowing manufacturers and retailers to rely on sales data from years past.

With an unpredictable event, the best thing to do is to be conservative when estimating demand, experts say. Err on the side of underproducing rather than overproducing. "It's almost like the stock market," says Jim Silver, editor-in-chief of timetoplaymag.com, an online reviews site for toys, baby products and sporting goods. "What's the key to success? Sell too early. Better to leave a few dollars on the table than the reverse."

If a business does find itself with dead stock, it may be able to return the unsold products to the manufacturer or unload them on a secondary market. For instance, former British colonies such as Hong Kong and India may still have an appetite for royal merchandise even after interest has waned in the United Kingdom, says Reibstein. Or the goods may trickle down from London's high street to smaller shops and sell for a discount there.

Unlike Harrod's, some large companies are not able to capitalize on such a short-lived event. Margaux Vega, a Fisher-Price spokesperson, says the toy company typically deals with 18-month lead times on manufacturing, making it impossible to turn out a tie-in product fast enough. "It's not something that Fisher-Price does," Vega says.

Fisher-Price does have a product that seems related to the prince's birth, the Royal Stepstool Potty. But this toddler-sized throne existed before the "royal baby frenzy" and was already popular, Vega says. She declined to comment on whether Fisher-Price had seen a recent spike in sales of the potty.

Small businesses have their own limitations. Should a startup find itself sitting on dead stock that it can't move, it may not be able to survive the loss. The sort of company best able to profit from fleeting consumer demand is a mid-sized company with healthy finances that can absorb a small loss if necessary, says Silver.

To estimate demand for royal baby-themed products, Reibstein recommends business owners look back to the 2011 royal wedding because both events will likely appeal to the same types of buyers.

How much risk you're willing to take to satisfy those buyers will depend on your product's profit margin. Reibstein gives the example of an item you produce for $20 and sell for $30. Since you will lose twice as much for each one you can't sell as you'll make from each one you can, it would be better to run out of inventory than to produce too much.

But if you're making a product for $20 and selling it for $120, says Reibstein, then it makes sense to risk outstripping demand. "Then I'm willing to err in the direction of overproducing five-to-one. I'd rather be stuck with five extra ones than have one that I didn't sell."

Brian Patrick Eha

Brian Patrick Eha is a freelance journalist and former assistant editor at Entrepreneur.com. He is writing a book about the global phenomenon of Bitcoin for Portfolio, an imprint of Penguin Random House. It will be published in 2015.